Inverse - ME 210 Applied Mathematics for Mechanical...

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ME – 210 Applied Mathematics for Mechanical Engineers Prof. Dr. Faruk Arınç Spring 2010 Inverse of a Square Matrix -1 Adj [A] [A] = det A Adjoint matrix of A Determinant of A Adj [A] = [C ij ] T Transpose of the Cofactor Matrix, [C ij ] T Cofactor Matrix: Matrix formed from cofactors of elements (minors with sign) Properties of matrix inversion: [A] [A] -1 = [A] -1 [A] = [I] {[A] -1 } -1 = [A] det{[A] -1 } = 1 / det[A] {[A] T } -1 = {[A] -1 } T {[B] [C]} -1 = [C] -1 [B] -1
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ME – 210 Applied Mathematics for Mechanical Engineers Prof. Dr. Faruk Arınç Spring 2010 Unique Solution of a Set of Linearly-independent, Algebraic Equations by Matrix Inverse [A] [x] = [b] [A] -1 [A] [x] = [A] -1 [b] or [x] = [A] -1 [b] Example 1 2 3 1 1 2 3 2 1 2 3 3 [x] [ ] [A] 2 2 2 2 1 2 2 10 3 5 1 10 3 5 3 1 1 1 3 b x x x x x x x x x x x x             Find the solution of the following system of linear equations by using matrix inverse.
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ME – 210
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This note was uploaded on 07/31/2011 for the course ME 210 taught by Professor Farukarinç during the Spring '09 term at Middle East Technical University.

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Inverse - ME 210 Applied Mathematics for Mechanical...

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